Copy UV scale within one object
How we usually go about matching the uv is to scale all the uv which are suppose to have the same materials together after matching the scale with Ctrl+A (Match island scale operation.) If this is impossible in a particular workflow. Then try the following:

We usually end up using a checker map pattern to eyeball the sizes of the checker, to approximate the scale of every surface before applying the actual material.


Create a color checker image go for 2048x2048
Apply the checker to all the surface of the model.
Enter Edit Mode and duplicate the faces in question and move it near the faces that has the scale you want to match. (Step for easier eyeball comparison)
Select the duplicated face in the UV Editor and start scaling.
Match the sizes in the checker pattern, and take note of the scaling factor
on the bottom left hand of the uv scale before hitting LMB .
Delete the duplicated face.
Enter the scale value from step 5. to the faces you want to affect.


If these answers are not satisfactory or understood, will be glad to post some images to help explain the workflow.